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01.06.2015 | Ausgabe 3/2015

Designs, Codes and Cryptography 3/2015

Fourier-reflexive partitions and MacWilliams identities for additive codes

Zeitschrift:
Designs, Codes and Cryptography > Ausgabe 3/2015
Autor:
Heide Gluesing-Luerssen
Wichtige Hinweise
Communicated by V. A. Zinoviev.

Abstract

A partition of a finite abelian group gives rise to a dual partition on the character group via the Fourier transform. Properties of this dualization are investigated, and a convenient test is given for when the bidual partition coincides with the primal partition. Such partitions permit MacWilliams identities for the partition enumerators of additive codes. It is shown that dualization commutes with taking products and symmetrized products of partitions on cartesian powers of the given group. After translating the results to Frobenius rings, which are identified with their character module, the approach is applied to partitions that arise from poset structures

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